Figurative sense of "to think over" is from late 14c.; to chew the rag "discusss some matter" is from 1885, apparently originally British army slang. Related: Chewed; chewing. To chew (someone) out (1948) probably is military slang from World War II. Chewing gum is by 1843, American English, originally hardened secretions of the spruce tree.

chew

n.

c.1200, "an act of chewing," from chew (v.). Meaning "wad of tobacco chewed at one time" is from 1725; as a kind of chewy candy, by 1906.